Luke tells us in verse 16 that it had been the regular custom for Jesus to go to the synagogue in Nazareth every Sabbath. There he would participate in some of its activities and one of the roles he engaged in was to read a passage of Scripture, which on that occasion was from the prophet Isaiah. When a person read a passage he did so standing, but when a passage was explained the teacher did so sitting. This method was followed by Jesus here.
It is not clear if Jesus followed the reading for the day or whether he selected his own passage. So we can view the choice of reading as providential in that it was connected to his reception of the Spirit which had taken place at his baptism. Or we can view the choice as deliberate, with Jesus wanting to explain to his fellow villagers what had happened to him in the period he was away from home.
In a sense, we base our Christian services on what took place in the synagogue every Sabbath. Ten adult males had to be present and men and women sat separate from one another, so if Jesus’ family was present his mother and sisters would not have sat with his brothers. In their service, there would be praise (singing of psalms), reading of Scripture, exposition of scripture, prayers and blessings (Benedictions).
We can deduce two details from what Jesus did here. First, he used the Bible to confirm who he was. In a sense, we can say that he was asking his listeners to check whether the report about him mentioned in verse 14 was according to the Scriptures.
Second, he wanted to participate in the public worship of God which at that time took place in the temple in Jerusalem or in synagogues located in different places. It would have been unthinkable for Jesus not to attend a local synagogue wherever he was on the Sabbath. And he is our example in the delight and diligence he showed in attending public worship.